Viscoelasticity and Preconditioning of Rat Skin Under Uniaxial Stretch: Microstructural Constitutive Characterization

Abstract

In spite of impressive progress in developing general constitutive laws for soft tissues, there exists still no comprehensive model valid for any general deformation scheme. The present study focuses on the uniaxial response of the skin as a model for other multifibrous soft tissues. While the skin's nonlinear viscoelastic constitutive response has been extensively studied and modeled, the phenomena associated with mechanical preconditioning have so far not been dealt with. Yet preconditioning is an inherent response feature in the skin, both in vitro and in vivo. It is hypothesized that by considering the structure of the elastic and collagen fibers and their individual rheological properties, it is possible to develop a reliable general constitutive law for the skin's uniaxial response. A stochastic hybrid constitutive model was developed based on the collagen and elastic fiber morphologies and their rheological properties. The multiple protocol uniaxial data of Eshel and Lanir ("Effects of Strain Level and Proteoglycan Depletion on Preconditioning and Viscoelastic Responses of Rat Dorsal Skin," 2001, Ann. Biomed. Eng., 29, pp. 164-172) served to estimate the model's parameters and to validate its reliability. Parametric investigation was then used to test model parsimony (minimal form) and to elucidate the roles of response mechanism and the relative contribution of each constituent. The model predictions show a very close fit to the data and good predictive capability. The results are consistent with the quasilinear viscoelastic response of both elastic and collagen fibers and are likewise consistent with the notion (supported by published experimental observations) that preconditioning in collagen is probably due to an increase in the fiber reference length and is due to strain softening (Mullins effect) in elastic fibers. The predictions also agree with the observed predominance of elastic fibers at low strains and suggest that as strain increases, collagen becomes predominant, but the effect of elastic fibers is still significant. The parsimony analysis of the 22 model parameters (18 are nonlinear in the model) points to the predominant role of viscoelasticity and preconditioning in both fibers, followed in order of importance by collagen waviness and elastic fiber nonlinearity. A reliable and comprehensive uniaxial constitutive law for the rat skin was developed based on the tissue microstructure and on its constituents' rheological properties.